In direct stiffness method, the beam and column connection are assumed to be done through center-line beam and column:
And hence we can represent them easily using frame elements ( 1D element) and do not have to model the surface contacts or using area elements.
However, in reality, beam and column may not always be connected via centerline: eg: such configuration is not uncommon
It is easy to see that the offset of beam shall induce additional moment on the supporting column.
How should I modify my stiffness matrix in order to accommodate the offset of beam from the column center location? The frame representation of beam and column is just too convenient to give up.
For the purpose of this question, assume that I am writing a frame analysis software from first principle ( yes, from the equations on the wiki page that I link to), and hence can't make use of any existing software package